{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/36768"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/36768","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Application of the Filtered-X LMS Algorithm for Disturbance Rejection in Time-Periodic Systems","abstract":"Extensive disturbance rejection methods have been established for time-invariant systems. However, the development of these techniques has not focused on application to time-periodic systems in particular until recently. The filtered-X LMS algorithm is regarded as the best disturbance rejection technique for aperiodic systems by many, as has been proven in the acoustics industry for rejecting unwanted noise. Since this is essentially a feedforward approach, we might expect its performance to be good with respect to time-periodic systems in which the disturbance frequency is already known. The work presented in this thesis is an investigation of the performance of the filtered-X LMS algorithm for disturbance rejection in time-periodic systems. Two cases are examined: a generalized linear, time-periodic system and the helicopter rotor blade in forward flight. Results for the generalized system show that the filtered-X LMS algorithm does converge for time-periodic disturbance inputs and can produce very small errors. For the helicopter rotor blade system the algorithm is shown to produce very small errors, with a 96%, or 14 dB, reduction in error from the open-loop system. The filtered-X LMS disturbance rejection technique is shown to provide a successful means of rejecting timeperiodic disturbances for time-periodic systems.","abstract_html":"Extensive disturbance rejection methods have been established for time-invariant systems. However, the development of these techniques has not focused on application to time-periodic systems in particular until recently. The filtered-X LMS algorithm is regarded as the best disturbance rejection technique for aperiodic systems by many, as has been proven in the acoustics industry for rejecting unwanted noise. Since this is essentially a feedforward approach, we might expect its performance to be good with respect to time-periodic systems in which the disturbance frequency is already known. The work presented in this thesis is an investigation of the performance of the filtered-X LMS algorithm for disturbance rejection in time-periodic systems. Two cases are examined: a generalized linear, time-periodic system and the helicopter rotor blade in forward flight. Results for the generalized system show that the filtered-X LMS algorithm does converge for time-periodic disturbance inputs and can produce very small errors. For the helicopter rotor blade system the algorithm is shown to produce very small errors, with a 96%, or 14 dB, reduction in error from the open-loop system. The filtered-X LMS disturbance rejection technique is shown to provide a successful means of rejecting timeperiodic disturbances for time-periodic systems.","abstract_has_math":false,"creators":["Fowler, Leslie Paige"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mechanical Engineering","degree_department":"Mechanical Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":["Robertshaw, Harry H."],"committee_members":["Saunders, William R.","Cudney, Harley H."],"year":1996,"date_issued":"1996-05-03","date_published":"1996-05-03","updated_at":"2026-07-22T22:19:12Z","subjects":["adaptive control","filtered-x LMS","time-periodic","disturbance rejection","helicopter rotor blade"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-5134151959631701"],"render_values":[{"text":"etd-5134151959631701","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/36768","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Robertshaw, Harry H."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Saunders, William R.","Cudney, Harley H."]},{"key":"dc:contributor.department","label":"Department","values":["Mechanical Engineering"]},{"key":"dc:creator","label":"Author","values":["Fowler, Leslie Paige"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T20:51:45Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T20:51:45Z","1996-05-03"]},{"key":"dc:date.issued","label":"Date","values":["1996-05-03"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["adaptive control","filtered-x LMS","time-periodic","disturbance rejection","helicopter rotor blade"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-5134151959631701"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/36768"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Extensive disturbance rejection methods have been established for time-invariant systems. However, the development of these techniques has not focused on application to time-periodic systems in particular until recently. The filtered-X LMS algorithm is regarded as the best disturbance rejection technique for aperiodic systems by many, as has been proven in the acoustics industry for rejecting unwanted noise. Since this is essentially a feedforward approach, we might expect its performance to be good with respect to time-periodic systems in which the disturbance frequency is already known. The work presented in this thesis is an investigation of the performance of the filtered-X LMS algorithm for disturbance rejection in time-periodic systems. Two cases are examined: a generalized linear, time-periodic system and the helicopter rotor blade in forward flight. Results for the generalized system show that the filtered-X LMS algorithm does converge for time-periodic disturbance inputs and can produce very small errors. For the helicopter rotor blade system the algorithm is shown to produce very small errors, with a 96%, or 14 dB, reduction in error from the open-loop system. The filtered-X LMS disturbance rejection technique is shown to provide a successful means of rejecting timeperiodic disturbances for time-periodic systems."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:title","label":"Title","values":["Application of the Filtered-X LMS Algorithm for Disturbance Rejection in Time-Periodic Systems"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Robertshaw, Harry H."],"dc:contributor.committeemember":["Saunders, William R.","Cudney, Harley H."],"dc:contributor.department":["Mechanical Engineering"],"dc:creator":["Fowler, Leslie Paige"],"dc:date.accessioned":["2014-03-14T20:51:45Z"],"dc:date.available":["2014-03-14T20:51:45Z","1996-05-03"],"dc:date.issued":["1996-05-03"],"dc:description.abstract":["Extensive disturbance rejection methods have been established for time-invariant systems. However, the development of these techniques has not focused on application to time-periodic systems in particular until recently. The filtered-X LMS algorithm is regarded as the best disturbance rejection technique for aperiodic systems by many, as has been proven in the acoustics industry for rejecting unwanted noise. Since this is essentially a feedforward approach, we might expect its performance to be good with respect to time-periodic systems in which the disturbance frequency is already known. The work presented in this thesis is an investigation of the performance of the filtered-X LMS algorithm for disturbance rejection in time-periodic systems. Two cases are examined: a generalized linear, time-periodic system and the helicopter rotor blade in forward flight. Results for the generalized system show that the filtered-X LMS algorithm does converge for time-periodic disturbance inputs and can produce very small errors. For the helicopter rotor blade system the algorithm is shown to produce very small errors, with a 96%, or 14 dB, reduction in error from the open-loop system. The filtered-X LMS disturbance rejection technique is shown to provide a successful means of rejecting timeperiodic disturbances for time-periodic systems."],"dc:description.degree":["Master of Science"],"dc:identifier.other":["etd-5134151959631701"],"dc:identifier.uri":["http://hdl.handle.net/10919/36768"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["adaptive control","filtered-x LMS","time-periodic","disturbance rejection","helicopter rotor blade"],"dc:title":["Application of the Filtered-X LMS Algorithm for Disturbance Rejection in Time-Periodic Systems"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:12Z"}